数学物理学报(英文版) ›› 2004, Vol. 24 ›› Issue (1): 118-128.
谭忠
TAN Zhong
摘要：
This paper considers the existence and asymptotic
estimates of global solutions and finite time blowup of
local solution of non-Newton filtration equation with special
medium void of the following form:
$$ \left\{
\begin{array}{ll}
\displaystyle \frac{u_t}{|x|^2}-\bigtriangleup_p u=u^q, & (x,t)\in\Omega\times (0,T),\\[2mm]
u(x,t)=0, & (x,t)\in\partial\Omega\times (0,T),\\
u(x,0)=u_0(x), & u_0(x)\geq 0, u_0(x)\not\equiv 0,
\end{array}\right.$$
where $\bigtriangleup_pu={\rm div}
\left(|\bigtriangledown u|^{p-2}\bigtriangledown u\right)$,
$\Omega$ is a smooth bounded domain in $R^N(N\geq 3$), $0\in\Omega$,
$2
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